Table of contents for Multivariable calculus : early transcendentals / James Stewart.


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Preface    xi
To the Student    xxi
0    PARAMETRIC EQUATIONS AND POAR COORD                 ATES      620
0.1   Curves Defined by Parametric Equations  621
Laboratory  Project  Running Circles around Circles  629
10.2  Calculus with Parametric Curves  630
Laboratory Project - Bizier Curves  639
10.3  Polar Coordinates  639
10.4  Areas and Lengths in Polar Coordinates  650
10.5  Conic Sections   654
10.6  Conic Sections in Polar Coordinates  662
Review    669
Problems Plus  672
I    INFINITE SEQUENCES AND SERIES            674
11.1  Sequences    675
Laboratory Project - Logistic Sequences  687
11.2  Series   687
11.3  The Integral Test and Estimates of Sums  697
1.4  The Comparison Tests  705
11.5  Alternating Series  710
11.6  Absolute Convergence and the Ratio and Root Tests  714
11.7  Strategy for Testing Series  72
11.8  Power Series   723
S1.9  Representations of Functions as Power Series  728
S110  Taylor and Maclaurin Series      734
Laboratory Project An Elusive Limit  748
Writing Project- How Newton Discovered the Binomial Series  748
11. 11  Applications of Taylor Polynomials     749
Applied  Project - Radiation from  the Stars  757
Review     758
Problems Plus   761
12    VECTORS AND THE GEOMETRY OF SPACE                       764
12.1   Three-Dimensional Coordinate Systems         765
12.2   Vectors    770
"12.3  The Dot Product      779
12.4   The Cross Product      786
Discovery Project - The Geometry of a Tetrahedron  794
12.5   Equations of Lines and Planes      794
Laboratory Project - Putting 3D in Perspective  804
12.6   Cylinders and Quadric Surfaces       804
Review     812
Problems Plus   815
--33, VECTOR FUNCTONS               816
13.1   Vector Functions and Space Curves       817
13.2   Derivatives and Integrals of Vector Functions     824
13.3   Arc Length and Curvature       830
13.4   Motion in Space: Velocity and Acceleration      838
Applied  Project  Kepler's Laws  848
Review      849
Problems Plus   852
114    I PARTIAL DERIVATIVES           854
14.1   Functions of Several Variables      855
14.2   Limits and Continuity      870
14.3   Partial Derivatives     878
14.4   Tangent Planes and Linear Approximations          892
14.5   The Chain Rule       901
14.6   Directional Derivatives and the Gradient Vector       910
14.7   Maximum and Minimum Values            922
Applied Project - Designing a Dumpster  933
Discovery Project - Quadratic Approximations and Critical Points  933
14.8   Lagrange Multipliers      934
Applied Project - Rocket Science  941
Applied Project - Hydro-Turbine Optimization  943
Review      944
Problems Plus   948
I5     MULTIPLE INTEGRALS              950
15.1   Double Integrals over Rectangles       951
15.2   Iterated Integrals    959
15.3   Double Integrals over General Regions        965
15.4   Double Integrals in Polar Coordinates       974
15.5   Applications of Double Integrals       980
15.6   Triple Integrals    990
Discovery Project. Volumes of Hyperspheres  1000
15.7   Triple Integrals in Cylindrical Coordinates 1000
Discovery Project * The  Intersection  of Three  Cylinders  1005
15.8   Triple Integrals in Spherical Coordinates      1005
Applied Project Roller Derby  1012
15.9   Change of Variables in Multiple Integrals       1012
Review      1021
Problems Plus    024
J 16  VECTOR CALCULUS          1026
16.1  Vector Fields  1027
16.2  Line Integrals  1034
16.3  The Fundamental Theorem for Line Integrals  1046
16.4  Green's Theorem   1055
16.5  Curl and Divergence  1061
16.6  Parametric Surfaces and Their Areas  1070
16.7  Surface Integrals  1081
16.8  Stokes' Theorem   1092
Writing Project  Three Men and Two Theorems  1098
16.9  The Divergence Theorem   1099
16.10 Summary    1105
Review    1106
Probiems Plus  11 09
-   7   SECOND-ORDER DIFFERENTIAL EQUATIONS                1 10
17.1  Second-Order Linear Equations  1111
17.2  Nonhomogeneous Linear Equations   1117
17.3  Applications of Second-Order Differential Equations  1125
17.4  Series Solutions  1133
Review    1137
"-    APPENDIXES        Al
F     Proofs of Theorems  A2
H     Complex Numbers    A5
I     Answers to Odd-Numbered Exercises  A13



Library of Congress subject headings for this publication: Calculus Textbooks, Transcendental functions Textbooks